论文标题
在prufer基地上的集体均匀空间上有足够的滑轮
Ample Sheaves on Group Homogeneous Spaces Over Prufer Bases
论文作者
论文摘要
在本说明中，我们研究了对群均匀空间及其增强性的可逆滑带，尤其是当基础是普力的方案时，即所有局部环都是评估环的方案。首先，我们为Hartogs的可逆滑轮现象提供了几个条件，以通过EGAIV4中的帕拉法（Egaiv4）配对来保持非弱方案，从而将相对有效的卡地亚分隔线描述为在估值环上的相对有效的卡地亚分隔剂，因为纯编码符号的平面封闭式封闭式集合。随后，我们获得了在非非素质情况下增强性的标准，从此，根据纯编成的纯循环明确地构造了充足的可逆滑轮。最后，我们建立了（半）充足的可逆滑带的扩展特性，这是在Prüferian底座上平滑的组均匀空间上的扩展特性。
In this note, we study invertible sheaves on group homogeneous spaces and their ampleness, especially when the bases are Prufer schemes, namely, the schemes whose all local rings are valuation rings. First, we give several conditions for Hartogs's phenomenon of invertible sheaves to hold on non-Noetherian schemes through parafactorial pairs in EGAIV4, thus describe relatively effective Cartier divisors on smooth schemes over valuation rings as flat closed subschemes of pure codimension one. Subsequently, we obtain criteria for ampleness in the non-Noetherian case, and from this, construct ample invertible sheaves explicitly in terms of the flat cycles of pure codimension one. Finally, we establish extension properties of (semi)ample invertible sheaves on group homogeneous spaces smooth over Prüferian bases.
